Deformation-induced coupling of the generalized external actions in third-gradient materials. (English) Zbl 1500.74008

Summary: In this study, diverse typologies of external actions are outlined, which turn out to be admissible for the third-gradient modeling of elastic materials. It is shown how such loading, when prescribed over the boundary surface, along the border edges and at the wedges of a deformable body in the Eulerian configuration, can be transformed into the Lagrangian description generating multiple interactions, with a surprising deformation-induced coupling. Such a phenomenon becomes more and more important at increasing the order of the \(\beta\)-forces, specified by duality as covectors expending work on the \(\beta\)th normal derivative of the virtual displacements, being herein at most \(\beta =2\). Insights are provided into the true nature of such generalized forces, resting on the differential geometric features of the deformation process.


74B20 Nonlinear elasticity
74A20 Theory of constitutive functions in solid mechanics
Full Text: DOI


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